The Total Amount Of Water A Tank Can Hold Is $14 \frac{1}{2}$ Gallons. Raul Wants To Find Out How Many $1 \frac{1}{4}$-gallon Buckets Of Water Can Be Used To Fill The Tank. Which Expressions Could Be Used To Represent This

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Understanding the Problem

When Raul wants to find out how many $1 \frac{1}{4}$-gallon buckets of water can be used to fill a tank that holds $14 \frac{1}{2}$ gallons, he needs to determine the number of buckets that can be filled with the total amount of water in the tank. This problem involves converting mixed numbers to improper fractions and performing division to find the solution.

Converting Mixed Numbers to Improper Fractions

To begin, we need to convert the mixed numbers to improper fractions. The total amount of water in the tank is $14 \frac{1}{2}$ gallons, which can be converted to an improper fraction as follows:

1412=(14×2)+12=28+12=29214 \frac{1}{2} = \frac{(14 \times 2) + 1}{2} = \frac{28 + 1}{2} = \frac{29}{2}

Similarly, the capacity of each bucket is $1 \frac{1}{4}$ gallons, which can be converted to an improper fraction as follows:

114=(1×4)+14=4+14=541 \frac{1}{4} = \frac{(1 \times 4) + 1}{4} = \frac{4 + 1}{4} = \frac{5}{4}

Representing the Problem with Expressions

Now that we have converted the mixed numbers to improper fractions, we can represent the problem with expressions. Let's assume that Raul wants to find the number of buckets that can be filled with the total amount of water in the tank. We can represent this as a division problem:

292÷54\frac{29}{2} \div \frac{5}{4}

This expression represents the number of buckets that can be filled with the total amount of water in the tank.

Simplifying the Expression

To simplify the expression, we can multiply the numerator by the reciprocal of the denominator:

292÷54=292×45\frac{29}{2} \div \frac{5}{4} = \frac{29}{2} \times \frac{4}{5}

This simplifies to:

29×42×5=11610=585\frac{29 \times 4}{2 \times 5} = \frac{116}{10} = \frac{58}{5}

Interpreting the Result

The result of the expression $\frac{58}{5}$ represents the number of buckets that can be filled with the total amount of water in the tank. To find the actual number of buckets, we can divide the numerator by the denominator:

585=11.6\frac{58}{5} = 11.6

Since we cannot have a fraction of a bucket, we can round down to the nearest whole number to find the number of buckets that can be filled:

11.6≈1111.6 \approx 11

Therefore, Raul can fill approximately 11 buckets with the total amount of water in the tank.

Conclusion

In this article, we explored how to represent the problem of finding the number of buckets that can be filled with the total amount of water in a tank. We converted mixed numbers to improper fractions, represented the problem with expressions, and simplified the expression to find the result. The result represents the number of buckets that can be filled with the total amount of water in the tank.

Understanding the Problem

In our previous article, we explored how to find the number of buckets that can be filled with the total amount of water in a tank. In this article, we will answer some frequently asked questions related to this problem.

Q: What is the total amount of water in the tank?

A: The total amount of water in the tank is $14 \frac{1}{2}$ gallons, which can be converted to an improper fraction as follows:

1412=(14×2)+12=28+12=29214 \frac{1}{2} = \frac{(14 \times 2) + 1}{2} = \frac{28 + 1}{2} = \frac{29}{2}

Q: What is the capacity of each bucket?

A: The capacity of each bucket is $1 \frac{1}{4}$ gallons, which can be converted to an improper fraction as follows:

114=(1×4)+14=4+14=541 \frac{1}{4} = \frac{(1 \times 4) + 1}{4} = \frac{4 + 1}{4} = \frac{5}{4}

Q: How can I represent the problem with expressions?

A: You can represent the problem with expressions by dividing the total amount of water in the tank by the capacity of each bucket:

292÷54\frac{29}{2} \div \frac{5}{4}

Q: How can I simplify the expression?

A: You can simplify the expression by multiplying the numerator by the reciprocal of the denominator:

292÷54=292×45\frac{29}{2} \div \frac{5}{4} = \frac{29}{2} \times \frac{4}{5}

This simplifies to:

29×42×5=11610=585\frac{29 \times 4}{2 \times 5} = \frac{116}{10} = \frac{58}{5}

Q: What does the result represent?

A: The result of the expression $\frac{58}{5}$ represents the number of buckets that can be filled with the total amount of water in the tank.

Q: How can I find the actual number of buckets?

A: You can find the actual number of buckets by dividing the numerator by the denominator:

585=11.6\frac{58}{5} = 11.6

Since we cannot have a fraction of a bucket, we can round down to the nearest whole number to find the number of buckets that can be filled:

11.6≈1111.6 \approx 11

Q: What if the tank is not full?

A: If the tank is not full, you can subtract the amount of water already in the tank from the total capacity of the tank to find the amount of water that needs to be filled.

Q: What if the buckets are not full?

A: If the buckets are not full, you can divide the amount of water in each bucket by the capacity of the bucket to find the number of buckets that can be filled.

Conclusion

In this article, we answered some frequently asked questions related to finding the number of buckets that can be filled with the total amount of water in a tank. We hope that this guide has been helpful in understanding the problem and finding the solution.

Additional Resources

If you have any further questions or need additional help, please refer to the following resources:

  • [Mathematics textbook]
  • [Online math resources]
  • [Mathematics tutor]

Disclaimer

The information provided in this article is for educational purposes only and should not be used as a substitute for professional advice. If you have any specific questions or concerns, please consult a qualified mathematics professional.